There appears to be some confusion here over the term "Moving Traffic Offence". As far as I'm aware, the term refers to those offences in which a vehicle must be moving in order to be committed (i.e. Traffic Light Offences, driving without due care, speeding etc.) you cannot commit these offences whilst a vehicle is stationary. This does not mean that you have to be specifically committing one of these offences in order for the police to pull you over though. There are a whole host of other motoring offences that can be committed regardless of whether a vehicle is moving or not, (Insurance offences, Licencing, Construction and use offences, Lighting regulation Offences etc.) and the Police have the power to pull you over for any such offence. For that matter, there are also a great many non motoring offences for which the Police also have the powers to pull a driver over, under the various forms of "stop and search" legislation.
A rear registration plate lamp is classified as an obligatory lamp under the Road Vehicle Lighting regulations 1989. Failure to fit a rear registration plate lamp therefore constitutes a fixed penalty offence (Obligatory lighting equipment not fitted - Conviction Code LR27). If the police suspect you to have committed this offence, then they do have the power to pull you over in order to serve you with a fixed penalty notice for that offence.
With regard to the breathalyser issue, under Part I, Section 6, of the Road Traffic act 1988 (Power to Administer Preliminary Tests), the Police have the power to pull over and obtain a breath specimen, if they suspect any driver has consumed alcohol. But they also have the power to obtain a specimen at the scene of a Road Traffic Collision, or if a moving traffic offence has been committed, even if they do not suspect alcohol to have been consumed. So, the Police do have the power to pull a driver over for a lighting regulation offence, or any other offence for that matter. However, they would not be able to obtain a breath specimen from the driver purely because they had committed that offence, as it is not a moving traffic offence. If however, having pulled the driver over for a non moving traffic offence, the officer then suspects that alcohol has been consumed (either due to the smell of alcohol or the drivers behavior), the Police then have the power to obtain a specimen.